The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c. What is the value of c?

If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then what is the value of b?

What is the equation of the straight line which is perpendicular to y = x and passes through (3, 2) ?

The straight lines x + y $$-$$ 4 = 0, 3x + y $$-$$ 4 = 0 and x + 3y $$-$$ 4 = 0 form a triangle, which is